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Cross-efficiency evaluation in Data envelopment analysis (DEA) has been accepted as a useful tool for performance evaluation and ranking of decision making units. However, the non-uniqueness of optimal weights in this evaluation has reduced the usefulness of this powerful method. As a result, it is recommended that secondary goals be introduced in cross-efficiency evaluation. Another issue in applying cross-efficiency DEA models is considering uncertainty in input and output variables. In this paper, the cross-efficiency model is modified to deal with stochastic data by applying chance-constrained approach. Some new stochastic DEA models and their associated deterministic versions are introduced. Furthermore, we discussed the existence of multiple weights in cross-efficiency method in the presence of stochastic data. As the result, we suggest some new secondary goals to better discriminate DMUs and obtain optimistic and pessimistic efficiency scores. Some numerical examples are used for illustration purposes.

Cross-efficiency Evaluation in Data Envelopment Analysis with Stochastic Data: A Chance-constrained Programming Approach